The massive black hole (BH) population in dwarf galaxies (M_BH_<~10^5^M_{sun}_) can provide strong constraints on the origin of BH seeds. However, traditional optical searches for active galactic nuclei (AGNs) only reliably detect high-accretion, relatively high-mass BHs in dwarf galaxies with low amounts of star formation, leaving a large portion of the overall BH population in dwarf galaxies relatively unexplored. Here, we present a sample of 81 dwarf galaxies (M_*_<=3x10^9^M_{sun}_) with detectable [FeX]{lambda}6374 coronal line emission indicative of accretion onto massive BHs, only two of which were previously identified as optical AGNs. We analyze optical spectroscopy from the Sloan Digital Sky Survey and find [FeX]{lambda}6374 luminosities in the range L_[FeX]_~10^36^-10^39^erg/s, with a median value of 1.6x10^38^erg/s. The [FeX]{lambda}6374 luminosities are generally much too high to be produced by stellar sources, including luminous Type IIn supernovae (SNe). Moreover, based on known SNe rates, we expect at most eight Type IIn SNe in our sample. That said, the [FeX]{lambda}6374 luminosities are consistent with accretion onto massive BHs from AGNs or tidal disruption events (TDEs). We find additional indicators of BH accretion in some cases using other emission line diagnostics, optical variability, and X-ray and radio emission (or some combination of these). However, many of the galaxies in our sample only have evidence for a massive BH based on their [FeX]{lambda}6374 luminosities. This work highlights the power of coronal line emission to find BHs in dwarf galaxies missed by other selection techniques and to probe the BH population in bluer, lower-mass dwarf galaxies.